Question: The $5$ points plotted below are on the graph of $y=\log_b{x}$. Based only on these $5$ points, plot the $5$ corresponding points that must be on the graph of $y=b^{x}$ by clicking on the graph. Click to add points
Explanation: Let's consider the point on $ y = \log_{ b}{ x}$ with coordinates $(D 2, 1 )$. Since $ y = { b}^ x$ is the inverse of $ y = \log_{ b}{ x}$, the point $( 1,D 2)$ is on the graph of $ y = { b}^ x$. In general, if $(D q, p )$ is on $ y = \log_{ b}{ x}$, then $( p,D q)$ is on $y={b}^ x$. For each point on $y=\log_b{x}$, we just switch the order of its coordinates to get a point on $y=b^x$. So, $y=b^x$ also has points with coordinates $(0,1)$, $(2, 4)$, $ (3, 8)$, and $(4, 16)$. Given the points that we know are on ${y=\log_b{x}}$, the graph below shows the $5$ points that must be on ${y=b^x}$. The original $5$ points are also plotted for reference. ${2}$ ${4}$ ${6}$ ${8}$ ${10}$ ${12}$ ${14}$ ${16}$ ${2}$ ${4}$ ${6}$ ${8}$ ${10}$ ${12}$ ${14}$ ${16}$ $y$ $x$